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Max Lübke 2021-10-18 11:56:38 +02:00
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@ -8,7 +8,7 @@ With this readme I will document all my steps I've done and will do.
- $\alpha$ - diffusion coefficient (dependent on species and direction(?)) - $\alpha$ - diffusion coefficient (dependent on species and direction(?))
- $h=1/M$ : with $M^2 = [0,1]^2$ - grid divided into parts between 0 and 1 - $h=1/M$ : with $M^2 = [0,1]^2$ - grid divided into parts between 0 and 1
(/spatial step/) (/spatial step/)
- $k=T/N$ : with $N = [0,T]$ - time steps per iteration (/time step/) - $k=T/N$ : with $N = [0,T]$ - time step size
- coefficients of the given equation from the paper are: - coefficients of the given equation from the paper are:
- $\alpha_xk/h^2$ in x direction - $\alpha_xk/h^2$ in x direction
- $\alpha_yk/h^2$ in y direction - $\alpha_yk/h^2$ in y direction
@ -23,3 +23,12 @@ parallelize but I will keep parallelization in mind.
Regarding the borders: I'm not quite sure what to do. Maybe it might be a good Regarding the borders: I'm not quite sure what to do. Maybe it might be a good
idea to use a simple gaussian kernel here to smooth those two columns and two idea to use a simple gaussian kernel here to smooth those two columns and two
lines. lines.
* Implementation
So currently I consider to implement the following methods for the module:
- +decompose matrix A into L and U+
- better use a library like Eigen here:
- using =SparseMatrix= to represent matrix $A$
- =SparseLU= to solve